Question

A long wire carrying current $i$ is placed close to a U-shaped conductor (of negligible resistance). A wire of length $l$ as shown in figure slides with a velocity $v$. Find the current induced in the loop as a function of distance $x$ from the current carrying wire to slider.

• A. $\frac{{\mu }_{0}ilu}{Rx}$
• B. $\frac{{\mu }_{0}ilu}{2\pi Rx}$
• C. $\frac{{\mu }_{0}ilu}{2Rx}$
• D. $\frac{{\mu }_{0}ilu}{4\pi Rx}$

Answer 1

Answer: (B)

$\frac{{\mu }_{0}ilu}{2\pi Rx}$

$B=\frac{{\mu }_{0}i}{2\pi x}$

$\epsilon =Blv=\frac{{\mu }_{0}ilv}{2\pi x}$

$I=\frac{\epsilon }{R}=\frac{{\mu }_{0}ilu}{2\pi Rx}$